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Relationship between funicular polygon and bending moment diagram

  1. Apr 26, 2012 #1
    Hello,

    I'm a civil engineering student.
    I learned how to contruct a funicular polygon and bending moment diagrams in two different subjects and I realised how close looking the two are, so I wondered if there was a good explanation to relate the two.

    I can feel it's kind of the same as the polygon represents the forces in order for the structure to be in equilibrum and the bending diagram represents how the structure bend in order to stay in equilibrum (is that right ?)

    Someone also told me yesterday that the slope of the funicular polygon has something to do with the shear force. I think it's because of the fact that the derivative of the bending moment is the shear force but I'm not sure why.

    Thank you in advance for your help!
     
  2. jcsd
  3. Apr 28, 2012 #2
    It can be proved using similar triangles that the funicular polygon is, to some scale, the bending moment diagram The scale comes from the polar diagram from which the funicular polygon is drawn. You might be able to work this out for yourself, since I have given you the clue. The consequences of this principle are huge for minimising the weights of structures. Most bridges have their dimensions determined by bending actions. The closer you can get to the funicular shape, the more efficient in materials the structure is likely to be (not necessarily minimum cost though). If you want to follow this up, the key words include 'line of thrust'. And shear force is the rate of change of bending moment (it can be proved from the definition "shear force at a section is the algebraic sum of forces on one side of the section and parallel to it")
     
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